Amoeba Can Solve TSP

A famous challenge in computer science is called “The Traveling Salesman Problem,” or TSP for sort. Scientists in Tokyo have found that a one-celled amoeba can solve TSP.

The problem goes like this:Suppose you are a traveling salesperson going from city to city to sell your goods. You want to maximize your efficiency to make as much money in as little time as possible. You want to find the shortest path that will let you hit every city on your route one time and return you to the starting point.

There is no simple mathematical formula to find the best route. The only way to solve the problem is to calculate the length of each possible route and see which is the shortest. The problem gets exponentially harder as more cities are added to the route. With four cities there are only three different routes to consider, but with six cities there are 360 different routes. If you had ten cities or more, the number of routes could be in the millions. With an increase in the number of cities, the number of routes increases logarithmically.

The traveling salesman problem is one of a broad class of problems computer scientists call “NP-hard.” (NP stands for nondeterministic polynomial time. People involved in hacking encrypted systems and mining cryptocurrency are interested in this sort of problem.)

At Keio University in Tokyo, scientists have discovered that an amoeba can solve TSP, with the help of some human ingenuity. They used a single-cell slime mold amoeba known as Physarum polycephalum which moves toward food and away from light. The scientists built a chamber filled with channels and placed some food at the end of each channel. The channels represent a city on the salesman’s route. The amoeba would extend tendrils into the channels to get the food. As it reached the food, a light would go on in that channel so that the amoeba would not go back to the same “city.”

The advantage is that that the amoeba doesn’t have to calculate every individual path as most computer algorithms do. Instead, the amoeba just reacts passively to the conditions and figures out the best possible arrangement by itself. What this means is that for the amoeba, adding more cities (channels) only increases the time linearly rather than logarithmically.

The lead study author Masashi Aono said, “The mechanism by which the amoeba maintains the quality of the approximate solution, that is, the short route length, remains a mystery.” If researchers can figure out how the amoeba can solve TSP, it could speed up our ability to solve all kinds of challenging computational problems.